--- a/src/seminorms.rs Sun Apr 27 15:03:51 2025 -0500
+++ b/src/seminorms.rs Thu Feb 26 11:38:43 2026 -0500
@@ -6,13 +6,15 @@
use crate::measures::{DeltaMeasure, DiscreteMeasure, Radon, SpikeIter, RNDM};
use alg_tools::bisection_tree::*;
+use alg_tools::bounds::Bounded;
+use alg_tools::error::DynResult;
use alg_tools::instance::Instance;
use alg_tools::iter::{FilterMapX, Mappable};
use alg_tools::linops::{BoundedLinear, Linear, Mapping};
use alg_tools::loc::Loc;
use alg_tools::mapping::RealMapping;
use alg_tools::nalgebra_support::ToNalgebraRealField;
-use alg_tools::norms::Linfinity;
+use alg_tools::norms::{Linfinity, Norm, NormExponent};
use alg_tools::sets::Cube;
use alg_tools::types::*;
use itertools::Itertools;
@@ -68,37 +70,37 @@
//
/// A trait alias for simple convolution kernels.
-pub trait SimpleConvolutionKernel<F: Float, const N: usize>:
- RealMapping<F, N> + Support<F, N> + Bounded<F> + Clone + 'static
+pub trait SimpleConvolutionKernel<const N: usize, F: Float = f64>:
+ RealMapping<N, F> + Support<N, F> + Bounded<F> + Clone + 'static
{
}
-impl<T, F: Float, const N: usize> SimpleConvolutionKernel<F, N> for T where
- T: RealMapping<F, N> + Support<F, N> + Bounded<F> + Clone + 'static
+impl<T, F: Float, const N: usize> SimpleConvolutionKernel<N, F> for T where
+ T: RealMapping<N, F> + Support<N, F> + Bounded<F> + Clone + 'static
{
}
/// [`SupportGenerator`] for [`ConvolutionOp`].
#[derive(Clone, Debug)]
-pub struct ConvolutionSupportGenerator<F: Float, K, const N: usize>
+pub struct ConvolutionSupportGenerator<K, const N: usize, F: Float = f64>
where
- K: SimpleConvolutionKernel<F, N>,
+ K: SimpleConvolutionKernel<N, F>,
{
kernel: K,
- centres: RNDM<F, N>,
+ centres: RNDM<N, F>,
}
-impl<F: Float, K, const N: usize> ConvolutionSupportGenerator<F, K, N>
+impl<F: Float, K, const N: usize> ConvolutionSupportGenerator<K, N, F>
where
- K: SimpleConvolutionKernel<F, N>,
+ K: SimpleConvolutionKernel<N, F>,
{
/// Construct the convolution kernel corresponding to `δ`, i.e., one centered at `δ.x` and
/// weighted by `δ.α`.
#[inline]
fn construct_kernel<'a>(
&'a self,
- δ: &'a DeltaMeasure<Loc<F, N>, F>,
- ) -> Weighted<Shift<K, F, N>, F> {
+ δ: &'a DeltaMeasure<Loc<N, F>, F>,
+ ) -> Weighted<Shift<K, N, F>, F> {
self.kernel.clone().shift(δ.x).weigh(δ.α)
}
@@ -108,21 +110,21 @@
#[inline]
fn construct_kernel_and_id_filtered<'a>(
&'a self,
- (id, δ): (usize, &'a DeltaMeasure<Loc<F, N>, F>),
- ) -> Option<(usize, Weighted<Shift<K, F, N>, F>)> {
+ (id, δ): (usize, &'a DeltaMeasure<Loc<N, F>, F>),
+ ) -> Option<(usize, Weighted<Shift<K, N, F>, F>)> {
(δ.α != F::ZERO).then(|| (id.into(), self.construct_kernel(δ)))
}
}
-impl<F: Float, K, const N: usize> SupportGenerator<F, N> for ConvolutionSupportGenerator<F, K, N>
+impl<F: Float, K, const N: usize> SupportGenerator<N, F> for ConvolutionSupportGenerator<K, N, F>
where
- K: SimpleConvolutionKernel<F, N>,
+ K: SimpleConvolutionKernel<N, F>,
{
type Id = usize;
- type SupportType = Weighted<Shift<K, F, N>, F>;
+ type SupportType = Weighted<Shift<K, N, F>, F>;
type AllDataIter<'a> = FilterMapX<
'a,
- Zip<RangeFrom<usize>, SpikeIter<'a, Loc<F, N>, F>>,
+ Zip<RangeFrom<usize>, SpikeIter<'a, Loc<N, F>, F>>,
Self,
(Self::Id, Self::SupportType),
>;
@@ -150,13 +152,13 @@
pub struct ConvolutionOp<F, K, BT, const N: usize>
where
F: Float + ToNalgebraRealField,
- BT: BTImpl<F, N, Data = usize>,
- K: SimpleConvolutionKernel<F, N>,
+ BT: BTImpl<N, F, Data = usize>,
+ K: SimpleConvolutionKernel<N, F>,
{
/// Depth of the [`BT`] bisection tree for the outputs [`Mapping::apply`].
depth: BT::Depth,
/// Domain of the [`BT`] bisection tree for the outputs [`Mapping::apply`].
- domain: Cube<F, N>,
+ domain: Cube<N, F>,
/// The convolution kernel
kernel: K,
_phantoms: PhantomData<(F, BT)>,
@@ -165,13 +167,13 @@
impl<F, K, BT, const N: usize> ConvolutionOp<F, K, BT, N>
where
F: Float + ToNalgebraRealField,
- BT: BTImpl<F, N, Data = usize>,
- K: SimpleConvolutionKernel<F, N>,
+ BT: BTImpl<N, F, Data = usize>,
+ K: SimpleConvolutionKernel<N, F>,
{
/// Creates a new convolution operator $𝒟$ with `kernel` on `domain`.
///
/// The output of [`Mapping::apply`] is a [`BT`] of given `depth`.
- pub fn new(depth: BT::Depth, domain: Cube<F, N>, kernel: K) -> Self {
+ pub fn new(depth: BT::Depth, domain: Cube<N, F>, kernel: K) -> Self {
ConvolutionOp {
depth: depth,
domain: domain,
@@ -181,7 +183,7 @@
}
/// Returns the support generator for this convolution operator.
- fn support_generator(&self, μ: RNDM<F, N>) -> ConvolutionSupportGenerator<F, K, N> {
+ fn support_generator(&self, μ: RNDM<N, F>) -> ConvolutionSupportGenerator<K, N, F> {
// TODO: can we avoid cloning μ?
ConvolutionSupportGenerator {
kernel: self.kernel.clone(),
@@ -195,18 +197,18 @@
}
}
-impl<F, K, BT, const N: usize> Mapping<RNDM<F, N>> for ConvolutionOp<F, K, BT, N>
+impl<F, K, BT, const N: usize> Mapping<RNDM<N, F>> for ConvolutionOp<F, K, BT, N>
where
F: Float + ToNalgebraRealField,
- BT: BTImpl<F, N, Data = usize>,
- K: SimpleConvolutionKernel<F, N>,
- Weighted<Shift<K, F, N>, F>: LocalAnalysis<F, BT::Agg, N>,
+ BT: BTImpl<N, F, Data = usize>,
+ K: SimpleConvolutionKernel<N, F>,
+ Weighted<Shift<K, N, F>, F>: LocalAnalysis<F, BT::Agg, N>,
{
- type Codomain = BTFN<F, ConvolutionSupportGenerator<F, K, N>, BT, N>;
+ type Codomain = BTFN<F, ConvolutionSupportGenerator<K, N, F>, BT, N>;
fn apply<I>(&self, μ: I) -> Self::Codomain
where
- I: Instance<RNDM<F, N>>,
+ I: Instance<RNDM<N, F>>,
{
let g = self.support_generator(μ.own());
BTFN::construct(self.domain.clone(), self.depth, g)
@@ -214,46 +216,67 @@
}
/// [`ConvolutionOp`]s as linear operators over [`DiscreteMeasure`]s.
-impl<F, K, BT, const N: usize> Linear<RNDM<F, N>> for ConvolutionOp<F, K, BT, N>
+impl<F, K, BT, const N: usize> Linear<RNDM<N, F>> for ConvolutionOp<F, K, BT, N>
where
F: Float + ToNalgebraRealField,
- BT: BTImpl<F, N, Data = usize>,
- K: SimpleConvolutionKernel<F, N>,
- Weighted<Shift<K, F, N>, F>: LocalAnalysis<F, BT::Agg, N>,
+ BT: BTImpl<N, F, Data = usize>,
+ K: SimpleConvolutionKernel<N, F>,
+ Weighted<Shift<K, N, F>, F>: LocalAnalysis<F, BT::Agg, N>,
{
}
-impl<F, K, BT, const N: usize> BoundedLinear<RNDM<F, N>, Radon, Linfinity, F>
+impl<F, K, BT, const N: usize> BoundedLinear<RNDM<N, F>, Radon, Linfinity, F>
for ConvolutionOp<F, K, BT, N>
where
F: Float + ToNalgebraRealField,
- BT: BTImpl<F, N, Data = usize>,
- K: SimpleConvolutionKernel<F, N>,
- Weighted<Shift<K, F, N>, F>: LocalAnalysis<F, BT::Agg, N>,
+ BT: BTImpl<N, F, Data = usize>,
+ K: SimpleConvolutionKernel<N, F>,
+ Weighted<Shift<K, N, F>, F>: LocalAnalysis<F, BT::Agg, N>,
{
- fn opnorm_bound(&self, _: Radon, _: Linfinity) -> F {
+ fn opnorm_bound(&self, _: Radon, _: Linfinity) -> DynResult<F> {
// With μ = ∑_i α_i δ_{x_i}, we have
// |𝒟μ|_∞
// = sup_z |∑_i α_i φ(z - x_i)|
// ≤ sup_z ∑_i |α_i| |φ(z - x_i)|
// ≤ ∑_i |α_i| |φ|_∞
// = |μ|_ℳ |φ|_∞
- self.kernel.bounds().uniform()
+ Ok(self.kernel.bounds().uniform())
}
}
-impl<F, K, BT, const N: usize> DiscreteMeasureOp<Loc<F, N>, F> for ConvolutionOp<F, K, BT, N>
+impl<'a, F, K, BT, const N: usize> NormExponent for &'a ConvolutionOp<F, K, BT, N>
+where
+ F: Float + ToNalgebraRealField,
+ BT: BTImpl<N, F, Data = usize>,
+ K: SimpleConvolutionKernel<N, F>,
+ Weighted<Shift<K, N, F>, F>: LocalAnalysis<F, BT::Agg, N>,
+{
+}
+
+impl<'a, F, K, BT, const N: usize> Norm<&'a ConvolutionOp<F, K, BT, N>, F> for RNDM<N, F>
where
F: Float + ToNalgebraRealField,
- BT: BTImpl<F, N, Data = usize>,
- K: SimpleConvolutionKernel<F, N>,
- Weighted<Shift<K, F, N>, F>: LocalAnalysis<F, BT::Agg, N>,
+ BT: BTImpl<N, F, Data = usize>,
+ K: SimpleConvolutionKernel<N, F>,
+ Weighted<Shift<K, N, F>, F>: LocalAnalysis<F, BT::Agg, N>,
{
- type PreCodomain = PreBTFN<F, ConvolutionSupportGenerator<F, K, N>, N>;
+ fn norm(&self, op𝒟: &'a ConvolutionOp<F, K, BT, N>) -> F {
+ self.apply(op𝒟.apply(self)).sqrt()
+ }
+}
+
+impl<F, K, BT, const N: usize> DiscreteMeasureOp<Loc<N, F>, F> for ConvolutionOp<F, K, BT, N>
+where
+ F: Float + ToNalgebraRealField,
+ BT: BTImpl<N, F, Data = usize>,
+ K: SimpleConvolutionKernel<N, F>,
+ Weighted<Shift<K, N, F>, F>: LocalAnalysis<F, BT::Agg, N>,
+{
+ type PreCodomain = PreBTFN<F, ConvolutionSupportGenerator<K, N, F>, N>;
fn findim_matrix<'a, I>(&self, points: I) -> DMatrix<F::MixedType>
where
- I: ExactSizeIterator<Item = &'a Loc<F, N>> + Clone,
+ I: ExactSizeIterator<Item = &'a Loc<N, F>> + Clone,
{
// TODO: Preliminary implementation. It be best to use sparse matrices or
// possibly explicit operators without matrices
@@ -268,7 +291,7 @@
/// A version of [`Mapping::apply`] that does not instantiate the [`BTFN`] codomain with
/// a bisection tree, instead returning a [`PreBTFN`]. This can improve performance when
/// the output is to be added as the right-hand-side operand to a proper BTFN.
- fn preapply(&self, μ: RNDM<F, N>) -> Self::PreCodomain {
+ fn preapply(&self, μ: RNDM<N, F>) -> Self::PreCodomain {
BTFN::new_pre(self.support_generator(μ))
}
}
@@ -277,27 +300,27 @@
/// for [`ConvolutionSupportGenerator`].
macro_rules! make_convolutionsupportgenerator_scalarop_rhs {
($trait:ident, $fn:ident, $trait_assign:ident, $fn_assign:ident) => {
- impl<F: Float, K: SimpleConvolutionKernel<F, N>, const N: usize> std::ops::$trait_assign<F>
- for ConvolutionSupportGenerator<F, K, N>
+ impl<F: Float, K: SimpleConvolutionKernel<N, F>, const N: usize> std::ops::$trait_assign<F>
+ for ConvolutionSupportGenerator<K, N, F>
{
fn $fn_assign(&mut self, t: F) {
self.centres.$fn_assign(t);
}
}
- impl<F: Float, K: SimpleConvolutionKernel<F, N>, const N: usize> std::ops::$trait<F>
- for ConvolutionSupportGenerator<F, K, N>
+ impl<F: Float, K: SimpleConvolutionKernel<N, F>, const N: usize> std::ops::$trait<F>
+ for ConvolutionSupportGenerator<K, N, F>
{
- type Output = ConvolutionSupportGenerator<F, K, N>;
+ type Output = ConvolutionSupportGenerator<K, N, F>;
fn $fn(mut self, t: F) -> Self::Output {
std::ops::$trait_assign::$fn_assign(&mut self.centres, t);
self
}
}
- impl<'a, F: Float, K: SimpleConvolutionKernel<F, N>, const N: usize> std::ops::$trait<F>
- for &'a ConvolutionSupportGenerator<F, K, N>
+ impl<'a, F: Float, K: SimpleConvolutionKernel<N, F>, const N: usize> std::ops::$trait<F>
+ for &'a ConvolutionSupportGenerator<K, N, F>
{
- type Output = ConvolutionSupportGenerator<F, K, N>;
+ type Output = ConvolutionSupportGenerator<K, N, F>;
fn $fn(self, t: F) -> Self::Output {
ConvolutionSupportGenerator {
kernel: self.kernel.clone(),
@@ -314,20 +337,20 @@
/// Generates an unary operation (e.g. [`std::ops::Neg`]) for [`ConvolutionSupportGenerator`].
macro_rules! make_convolutionsupportgenerator_unaryop {
($trait:ident, $fn:ident) => {
- impl<F: Float, K: SimpleConvolutionKernel<F, N>, const N: usize> std::ops::$trait
- for ConvolutionSupportGenerator<F, K, N>
+ impl<F: Float, K: SimpleConvolutionKernel<N, F>, const N: usize> std::ops::$trait
+ for ConvolutionSupportGenerator<K, N, F>
{
- type Output = ConvolutionSupportGenerator<F, K, N>;
+ type Output = ConvolutionSupportGenerator<K, N, F>;
fn $fn(mut self) -> Self::Output {
self.centres = self.centres.$fn();
self
}
}
- impl<'a, F: Float, K: SimpleConvolutionKernel<F, N>, const N: usize> std::ops::$trait
- for &'a ConvolutionSupportGenerator<F, K, N>
+ impl<'a, F: Float, K: SimpleConvolutionKernel<N, F>, const N: usize> std::ops::$trait
+ for &'a ConvolutionSupportGenerator<K, N, F>
{
- type Output = ConvolutionSupportGenerator<F, K, N>;
+ type Output = ConvolutionSupportGenerator<K, N, F>;
fn $fn(self) -> Self::Output {
ConvolutionSupportGenerator {
kernel: self.kernel.clone(),